Now comes news (originally from The Verge) that Microsoft is working on a shrunken-down, media streaming-friendly set-top box for television and sound systems — “a low-cost alternative to its Xbox console, designed to provide access to core entertainment services.”

Basically, this would be an entry-level XBox for casual gaming (building on Microsoft’s home gaming strength), music and videos (places where Microsoft needs work).

Microsoft would not confirm that it was working on the so-called Xbox TV, and didn’t mention any such thing when we met with the company’s music team in Manhattan last month. And it’s not clear whether Microsoft intends this to have its own controller, or whether the phone would be cable of streaming music to the device, or even remote controlling its music service.

Most other follow-up stories are focusing on the video streaming or gaming aspects, but rest assured — if Microsoft releases an ‘Xbox Lite’/’Xbox TV’ device, it will integrate with Microsoft’s Spotify competitor, XBox Music. Of course the idea of a lightweight media streamer that integrates tightly with Windows Phone (and possibly other devices) is a good one, and it shows that Microsoft is intent on copying Apple’s in-home strategy, the same way Android copied much of its mobile strategy.

In addition to media (typically music and movies) streaming, The Verge’s Microsoft source says Xbox TV will also let you play “casual” games — stuff like Words with Friends. It will apparently boot up quickly, which means it will work well as a music-streaming device.

Music, casual games, videos on both screens… this is right where Apple is going with iOS via AirPlay, where Google recently signalled its intent on doing the same, and where we believe the next digital entertainment battle will be pitched: in the home (meaning the same music, games, and videos across every digital device in the home, and on mobile devices — one multi-pronged thing of all stuff, everywhere).

Microsoft Xbox TV or whatever it’s called, regardless of whether it’s a commercial success initially, will give Microsoft an important placeholder in this race to the home, by way of the living room, by way of whatever companies can use to get there — whether that means a dominant mobile OS or a dominant gaming console.